Guys, So let's check out this problem here. We have hikers who start at the bottom of a mountain. So basically, I'm going to call this point A like this. And they're trying to get to the top of this mountain, so I'm going to call this point B. But instead of taking a straight path, like up like this, and therefore kind of looking like an inclined plane, what's actually happening is this hiker is going to take an irregular path with varying speeds and also inclinations. So what those would look like is kind of like a squiggly path to get up to the top here of this mountain. We want to do is we want to figure out the work that is done by gravity on the hiker during this entire hike. So basically, this is what I'm going to do. I'm going to draw a little line like this, and we know that this height here of the mountain, this is going to be my delta y, is going to be 1,000 meters. But the path that I'm taking from A to B is actually going to be sort of not straight. It's going to be curvy like this. So how do I calculate the work that's done by gravity? Well, remember that the equation is just
Wg = - mg × Δyand what we have to do is we have to figure out a direction first of positive. So because I'm going from the bottom to the top, I'm going to call the upward direction positive like this. So what this means is that our delta y is actually positive 1,000 here. So if we get to the equation
Wg = negative mg × Δy, we run into a problem here because you might think that as we go along this path here, the work that's done is going to be sort of changing, and you're actually right. It is. At any point along the path right here for this hiker, we know that the mg is going to point downwards. However, one of the really cool things about the work that's done by gravity is from the equation, we can tell that the work done only really depends on delta y. It's only dependent on the change in the height here. So the work that's done by gravity depends only on the change in your height, and it doesn't actually cause it doesn't actually depend on the path it's taken. So you wouldn't be able to solve this problem if you didn't know this. So this is actually called path independence. You might see that in your textbooks. It basically just means that it doesn't matter what path you take. All that matters is that you started at A and ended at B and the difference between those two is 1,000 meters. So the work that's done by gravity is just going to be negative. We have 75 times 9.8, and then we're going to multiply this by positive 1,000. So as we should expect, the work done by gravity is going to be negative, and it's going to be 735,000 joules. That's the work that is done by gravity. Alright? So again, only just depends on the height. It doesn't actually matter the path that you take here. We'll talk about that more, in a later video. So that's it for this one, guys.